Solar structureThe Problem
The ResolutionMHD turbulence
References
Coronal Heating Problem
Mani Chandra Arnab Dhabal Raziman T V
PHY690C Course Project
Indian Institute of Technology Kanpur
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Outline
1 Solar structure
2 The Problem
3 The ResolutionSource of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
4 MHD turbulenceSpectrum: Kolmogorov or Kraichnan?
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Structure
Source: Wikimedia commons
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Zones
The Core
Upto 0.25 Solar radiiNuclear fusion occursTemperature as high as 13 million K
Radiative zone
0.25-0.7 solar radiiThermal radiation transfers heat energy outwardsTemperature falls from 7 million K to 2 million K
Convective zone
0.7-1 solar radiiPlasma not dense or hot enough for radiationThermal convections carries heat outwards
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Zones
Photosphere
Visible surface of the sunBelow the photosphere sun is opaqueTemperature between 4500-6000K
Chromosphere
About 2000 km thickTemperatures upto 20,000 K
Corona
Extends to millions of kilometersTemperature ranges from 1 to 3 million K
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Temperature variation
Source: Wikimedia commons
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
From the core to the photosphere, temperature decreases
However, beyond the photosphere the temperature increases
Second law of thermodynamics : Heat cannot �ow from a cold
body to a hot body
Coronal temperature more than two orders of magnitude
higher than photosphere
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Essence
How does the corona maintain such high temperatures?
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Source
Less of a matter of contention
Photospheric and subphotospheric motions
Footpoints of coronal loops
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Mechanism
The �Real� problem
Many candidate processes have been proposed
No consensus yet
More accepted mechanisms involve MHD turbulence
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Acoustic waves
Surface convection zones create a spectrum of acoustic waves
Density decrease in outer atmosphere results in rapid increaseof amplitude
Shock formation → Shock dissipation heats outer stellar layers
Shockless dissipation possible with radiative heating andionisation pumping
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Magnetoacoustic body waves
Found in the bulk of the �uid
Slow mode and fast modes : Compressible modes
Slow mode waves can dissipate via shocks
Fast mode waves can dissipate via Landau damping
Particles with velocities similar to the wave velocity canexchange energy with the wave. This can transfer energy fromthe wave to the plasma
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Alfvén body waves
Incompressible modes
Various dissipation mechanisms
Mode coupling: Transfer of energy to other modes whichdissipate more readilyResonant heating: Constructive interference of the re�ectedand propagating Alfvén wavesLandau dampingTurbulent heating: Kolmogorov-type cascadeViscous heating
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Surface waves
At boundaries between media
Dissipation mechanisms
Resonant absorption: Kinetic waves receive energy fromsurface wavesMode couplingPhase mixing
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Currents and �elds
Currents and magnetic �elds carry energy
Current sheets
Dissipations of currents:
Joule heatingNano�ares: Small �are events which happen in the coronaMagnetic reconnection
Source: Scholarpedia
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Active regions
Ensembles of loop structures connecting points of oppositemagnetic polarity in the photosphere
Location of phenomena linked to magnetic �elds
Heating requirement: 2×102−2×103W /m2
Compose 82.4% of total heating requirements
Low Alfvén timescales : DC processes are dominant
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Quiet-sun regions
�Normal� regions
Heating requirement: 1×101−2×102W /m2
Compose 17.2% of total heating requirement
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Coronal holes
Coronal regions that are dark in X-rays
Fast solar wind leaves the corona through coronal holes
Heating requirement: 5×100−1×101W /m2
Compose 0.4% of total heating requirement
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Coronal losses
Mainly three sources
Emission in resonance lines of ionized metals
Radiative recombinations due to the most abundant coronalions
Bremsstrahlung radiation at high temperatures
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Source of the energyMechanism of energy dissipationProposed mechanismsRegions of the corona
Coronal losses
The total radiation loss per unit volume
L= nenHP(T )
ne = nH = 2×108cm−3, P(T ) = 10−21.94
L∼ 5×107W /m3
∼ 300W per unit area
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Spectrum: Kolmogorov or Kraichnan?
MHD turbulence
Widely agreed to be leading a major role in coronal heatingprocess
Disagreement on whether the spectrum is Kolmogorov orKraichnan
Both found in literatureKraichnan: Dmitruk & GómezKolmogorov: Chae et al.
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Spectrum: Kolmogorov or Kraichnan?
Kolmogorov Flux
Energy �ux:
E (k)∼ Cε23 k
−53
kE (k)∼ Cε23 k
−23
U2 ∼ Cε23 k
−53
Energy dissipation rate per unit mass
ε ∼ U3
L
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Spectrum: Kolmogorov or Kraichnan?
Power dissipated per unit area:
P ∼ ρU3Lo
L
(L0 is the thickness of the corona)
Putting in numbers : ρ = 10−12kg/m3, U = 50km/s,L0 = 7×108m, L= 2×105km
We get P ∼ 400W /m2
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Spectrum: Kolmogorov or Kraichnan?
Kraichnan Flux
E (k) ∼ A(εB0)12 k
−32
kE (k) ∼ A(εB0)12 k
−12
U2 ∼ ε12B0
12 k
−12
ε ∼ U4
B0L
P ∼ ρU4Lo
LB0
The Kraichnan �ux is found to be U
B0times the Kolmogorov �ux.
In the active regions, we have a large magnetic �eld around 1000G.
This gives P ∼ 0.2W /m2
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Spectrum: Kolmogorov or Kraichnan?
Comparison
Kolmogorov �ux calculated falls in active region requirementrange
Kraichnan �ux falls below requirement
More �ne-tuning required for numbers?
Similar calculation in Chae et al.:
Kolmogorov turbulence suggests an injection scale length of~1200kmKraichnan injection scale length ~15kmKolmogorov-type turbulence is more preferred
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Acknowledgements
We would like to thank Dr. M.K. Verma for guiding us through theproject. Our sincere thanks to our classmates for their presentationfeedback,
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Bibliography I
Markus J. Aschwanden.An Evaluation of Coronal Heating Models for Active RegionsBased on Yohkoh, SOHO, and TRACE Observations.The Astrophysical Journal, Volume 560, Issue 2, pp. 1035-1044.
Udo; Lemaire Chae, Jongchul; Schühle.SUMER Measurements of Nonthermal Motions: Constraints onCoronal Heating Mechanisms.The Astrophysical Journal, Volume 505, Issue 2, pp. 957-973.
Daniel O. Dmitruk, Pablo; Gómez.Scaling Law for the Heating of Solar Coronal Loops.The Astrophysical Journal, Volume 527, Issue 1, pp. L63-L66.
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Bibliography II
Daniel O.; Martens Milano, Leonardo J.; Gomez.Solar Coronal Heating: AC versus DC.Astrophysical Journal v.490, p.442-451, 20 November 1997.
P. Narain, U.; Ulmschneider.Chromospheric and coronal heating mechanisms.Space Science Reviews, vol. 54, Dec. 1990, p. 377-445.
P. Narain, U.; Ulmschneider.Chromospheric and Coronal Heating Mechanisms II.Space Science Reviews, Volume 75, Issue 3-4, pp. 453-509.
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem
Solar structureThe Problem
The ResolutionMHD turbulence
References
Bibliography III
P.; Matthaeus Oughton, S.; Dmitruk.Coronal Heating and Reduced MHD.Turbulence and Magnetic Fields in Astrophysics. Edited by E.
Falgarone, and T. Passot., Lecture Notes in Physics, vol. 614,
p.28-55.
Wikipedia.Coronal radiative losses � Wikipedia, the free encyclopedia,2011.[Online; accessed 14-April-2011].
Wikipedia.Sun � Wikipedia, the free encyclopedia, 2011.[Online; accessed 14-April-2011].
Mani Chandra, Arnab Dhabal, Raziman T V Coronal Heating Problem